a basket contains 5 red balls, 3 blue balls, 1 green balls

what is the probability of getting 2 red balls, 1 blue ball and 1 green ball if a sample of 4 balls are taken from the basket.

How do i start solving this problem.

Please help.

Hi "i like c",

there are 2 ways to work it out, if not more...

If a sample of 4 balls are taken,

we can list the order of selection if they are chosen one-by-one.

RRBG red 1st, red 2nd, blue 3rd, green 4th.... \(\displaystyle P=\frac{5}{9}\ \frac{4}{8}\ \frac{3}{7}\ \frac{1}{6}\)

RRGB

RBRG

RBGR

RGRB

RGBR

GRRB

GRBR

GBRR

BRRG

BRGR

BGRR

If you calculate the remaining probabilities and sum them, you will have the

probability of choosing 2 reds, 1 blue and 1 green.

Alternatively there are \(\displaystyle \binom{9}{4}\) ways to choose 4 from 9.

There are \(\displaystyle \binom{5}{2}\) ways to choose 2 reds

There are \(\displaystyle \binom{3}{1}\) ways to choose one blue and only 1 way to choose the green.

Any 2 reds can go with any blue, hence we multiply those numbers of ways

to find the total number of ways we can get 2 reds, 1 blue and 1 green

Hence you divide that number by the total number of ways to choose 4 from 9.